Method and apparatus for radio location

ABSTRACT

This disclosure relates to multi-element antenna clusters or arrays for the reception and transmission of radio waves for direction-finding, navigation aid and emitter and/or receiver location purposes. In particular, it relates to arrangements of multiple antennas whereby the direction of propagation (arrival or departure) of a wavefront is determined from a combination of the amplitudes of phasor (or total individual antenna output) differences between pairs of antennas, said arrangements being along certain geometrical patterns, such as a circle, an ellipse, a polygon, an open straight line, etc., with at least one longest dimension measuring more than one wavelength of the incident or departing wave. Although described in terms of electromagnetic waves and hence antennas as receiving sensors or radiators, this invention in reality applies to any other form of propagating waveborne energy, such as acoustic, ultrasonic, seismic, etc.

This application is a continuation of application Ser. No. 07/767,883,filed Sep. 30, 1991, abandoned, which in turn is a division ofapplication Ser. No. 07/524,600, filed May 17, 1990, now U.S. Pat. No.5,084,709.

BACKGROUND OF THE INVENTION

This invention relates to multi-element sensor or radiator arrays forthe reception or emission of propagating waveborne energy for thepurpose of determining or communicating the direction of propagation ofthe wavefront, or for providing a navigation-aid beacon, or fordetermining the location of a distant emitter or of the sensing orreceiving apparatus. In particular, it relates to arrangements in whichthe total phasor difference between the outputs of pairs of elements,rather than just the phase difference, is taken, its amplitude isdetected, and the result is used to determine the direction informationof interest. It also relates to arrangements in which both saidamplitude and said phase difference are used.

Prior art arrangements of multiple sensor elements are well-known inwhich the direction information is obtained by first taking the phasordifferences between the outputs of individual sensor elements. Sucharrangements of four or more elements are as a matter of course aroundthe perimeter of a circle of diameter that at most is substantiallyequivalent to one wavelength of the subject wave, and by deliberate andcalculated design is intended not to exceed this maximum allowableextent. Such arrays are commonly referred to in the art as Adcockantennas, Adcock arrays or structures, or simply Adcocks. In sucharrays, the outputs of diametrically separated antenna pairs aredifferentially combined, although other pairings have been suggested.This method of combining the outputs of two separated antennas is knownto yield a phasor-difference signal whose amplitude carries thetrigonometric sine of the phase-shift difference between said twooutputs of separated antennas, and whose phase is free of any dependenceon the direction of propagation of the signal wavefront. For spacing ofup to no more than just one wavelength between two antennas whoseoutputs are differentially combined, the azimuth and elevation angles ofthe Poynting vector of the propagating wavefront can be calculated fromthe detected phasor-difference amplitudes of two or more pairs ofantenna elements arranged around a circle. However, it is universallypresumed in the prior art of Adcock arrays that an uncorrectable errordue to spacing between antenna pairs results and renders the arrayoutputs unusable for direction finding for signal frequencies at whichthe diameter of an Adcock array exceeds a wavelength. This limitation ofthe diameter to a wavelength or less condemns Adcocks to beingsmall-aperture sensors, and to a severe limitation on achievabledirection-finding instrument precision and system performance accuracythat are characteristic of small apertures.

It is therefore an object of this invention to avoid the limitations ofa small aperture on instrumental precision and performance accuracy byarranging the discrete sensor or radiator elements around a circle witha diameter well in excess of one wavelength. It is well known that thegreater the aperture (or the largest linear dimension, such as thelength of a linear array, the diameter of a circular array, the majoraxis of an elliptical array, and so forth) of an array, the higher theprecision and accuracy achievable in the use of the array to determinethe direction of propagation of a wavefront.

In certain situations, directions of approach or departure are not allof equal likelihood or importance, certain sectors being favored overothers for one reason or another. In certain other situations, mountingplatform or space limitations allow greater extensions of the elementseparations in certain directions than in others, which would rule outarrangement of the discrete elements around circles of diameters equalto the longest available dimension.

It is therefore another object of this invention to determine thedirection of propagation of a traveling wavefront from the phasordifferences of the outputs of more than one pair of sensor or radiatorelements that are arranged along noncircular patterns or rows thatconform to specified directional preferences or to available space thatlacks circular symmetry.

It is yet a further object of this invention when employing circulararrays of elements (i.e., discrete sensors or discrete radiators) toachieve the favoring of a particular sector of directions by derivingthe direction to be determined within said sector from a combination ofelement-output phasor differences between nondiametrically separatedpairs of elements that are symmetrically positioned relative to the axisof said sector, together with the phasor difference of the outputs ofthe pair of elements separated by the diameter along said axis.

One additional consideration addressed by the present invention is thefact that the successful determination of the direction of propagationof a signal wave from the amplitude of the phasor difference, or fromthe phase difference, between the outputs of two separated sensorelements is predicated in the prior art on said signal comprising, inthe form it is found when intercepted, a filter-separable pure sinwave.While this condition is satisfied by most common signal types, there hasmore recently been a growing interest in suppressed-carrierspectrum-spread-carrier signals, such as wideband analog or digitalFM(e.g., linear-ramp FM, high-deviation-ratio FM by random noise,frequency hopping spread-spectrum) and other (e.g., direct-sequencephase-reversal modulated) signals of all types that do not present afilter-separable-discrete sinusoidal component on arrival.

It is therefore a further object of this invention to provide means foroperating on spectrum-spread and suppressed-carrier signal outputs ofelements in an array to derive therefrom sinusoidal-phasor differencesand sinusoid-pair phase differences that correspond to what would beobtained if such sinusoid were present as a discrete spectral line insaid signal on arrival.

These and other objects and features of this invention will becomeapparent from the claims, and from the following description when readin conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings:

FIGS. 1A and 1B illustrate receiving structures that feature the majorfunctional components of Adcock-type signal receiving and processingpreparatory to the determination of direction-of-arrival of an incidentwavefront.

FIGS. 2a-2(e) illustrate a number of alternative array configurationsand antenna pairing arrangements for effecting increased sensor arrayaperture in a particular preferred direction angle sector, in accordancewith this invention.

FIGS. 3a and 3b illustrate the use of the sense antenna output to effectspectrum-despreading of a spectrally spread incident signal down to asingle-frequency, filter-separable component, in accordance with thisinvention.

DETAILED DESCRIPTION

With reference to FIG. 1, it is well-known that an Adcock array consistsofa number of separate antenna elements, 1 (designated N, E, S and W,for a four-element array, plus others in between, for a higher-orderarray, in FIG. 1a), that are arranged with uniform spacing around acircle of diameter restricted to well below one wavelength of the signalwave for which it is to be used, for a low-order (8-element or less)array, and to nominally one wavelength, for a higher-order (more than8-element) array, wherein the outputs of diametrically opposed pairs ofantennas are subtracted one from the other, by means 3, to obtain theirphasor differences 4, which are then passed on via 5, or 8, 9 and 10 toamplitudedetection means followed by direction-determination processingmeans. Direction finding based on such arrays is plagued with lowprecision and accuracy characteristic of the very small aperture(diameter) necessary toensure very approximately linear dependence ofthe amplitudes of the resultant N-S and E-W phasor-difference outputsupon the cosine and sine of the azimuth of arrival, and hence negligiblespacing errors.

Increasing the diameter of the array circle from less than a quarter ofa wavelength up to one wavelength is made possible by increasing thenumber of elements in the array (i.e., the order of the array). Thedirection-dependent amplitude patterns of the phasor-difference outputsofpairs whose connecting axes are offset relative to one another combineto fill out one another's pattern major lobe fall-off with angle awayfrom their respective axes as the diameter of the pattern circle isincreased, thereby reducing the error in direction determination due toincreased spacing between antenna pairs. At a value of the spacing equalto about 1.22×wavelength, a catastrophic breakdown in directiondeterminationis experienced, expressible by an irreducible error due tospacing. Prior art practice has been firmly based on the assumption thatthe 1.22 wavelength spacing represents an absolute upper bound on thediameter of an Adcock array beyond which such an array becomes unusable.It will be shown in this disclosure that said prior art assumption isinvalid, and that Adcock-type (henceforth, A-type) arrays of circular aswell as noncircular forms including separations between paired antennasin excess of said prior art Adcock-array limit will providedirection-finding performance precision and accuracy that are superiorto those realizable with prior art Adcock arrays. Moreover, themagnitude of the irreducible error at the breakdown values of antennaspacing is π/2 rad, and it canbe calibrated out.

The mechanism by which an increase in the Adcock array diameter from asmall fraction of a wavelength to about one wavelength is made possiblecan be utilized to synthesize phasor-difference amplitude patterns basedon larger antenna-pair separations for improved direction-findingperformance, selectively and nonselectively in direction. Directionallynonselective direction finding is provided by circular arrayarrangements with pairings of diametrically separated antennas.Directionally preferential direction finding is obtained with a circulararray by pairing nondiametrically separated antennas, as shown solelyfor illustration in FIG. 2a). Directionally preferential directionfinding canalso be obtained by employing noncircular array arrangements,such as shownsolely for illustration in FIG. 2b).

Attention will now be directed in this proposal to showing how to evolvenew methods and apparatus for improving instrumental precision andperformance accuracy in direction finding by means of Adcock-type arrayswith circular apertures in excess of one wavelength, and by structuringthe receiver for robust processing of Adcock-pair difference-signals. Westart by reformulating the basic theory in order to a) show how bothazimuth and elevation angle of arrival can be derived from theamplitudes of the Adcock-pair difference signals; and b) bring out thebases for, andthe conditions under which, an Adcock-type antenna clustercan be effectively configured with apertures well in excess of onewavelength. The discussion is then directed to structuring the receiverto ensure instrumental stability and low associated systematic errors.Finally, the additional receiver functional-structural requirements arespecified for application to signals of wide-band modulationcharacteristics, such as wide band-spreading FM, and direct-sequence andfrequency-hopping spread spectrum.

Direction of arrival(or DOA) measurement by means of a 4-element Adcockcluster is based on the properties of the phasor difference between theoutputs of diametrically separated Adcock-paired (henceforth, A-paired)vertically polarized antennas. These properties are brought out by firstnoting, with reference to FIGS. 1a), 2, that in response to an incidentsingle-frequency sinusoid, cos ω_(c) t, the difference betweentheoutputs of the N and S antennas, is given by

    E.sub.s cosαcos{ω.sub.c t-(πD/λ.sub.c)cosαcosθ} (N output)

    -E.sub.s cosαcos{ω.sub.c t+(πD/λ.sub.c)cosαcosθ}-(S output)

    =2E.sub.s cosαsin{(πD/λ.sub.c)cosαcosθ}sinω.sub.ct

    .tbd.e.sub.NS (t)≡E.sub.s A.sub.NS (α,θ)sinω.sub.c t                                                         (1)

where, with reference to FIG. 1a), 2,

α=elevation angle of arrival of the incident wavefront, relative to theplane of the Adcock cluster

θ=Azimuth angle of arrival of the incident wavefront, relative to theN-Saxis

D=distance (diameter of cluster circle) between the two antennas

λ_(c) =(2π/ω_(c))c=wavelength of incident wave

E_(s) =Amplitude of signal out of each antenna when α=O

Similarly, for the E and W antenna pair,

    e.sub.EW (t)≡2E.sub.s cosαsin{(πD/λ.sub.c)cosαsinθ}sinω.sub.c t≡E.sub.s A.sub.EW (α,θ)sinω.sub.c t (2)

In discussions directional sensing characteristics, we shall refer toA_(NS) (α,θ) and A_(EW) (α,θ) as the N-S and E-W polar patterns of theAdcock cluster. In discussions of the signals out of the A-pairs, weshall refer to them as the direction-dependent amplitude (or DDA)factors.

Determination of bearing, or azimuth, angle is based on the fact that

    e.sub.EW (t)/e.sub.NS (t)=A.sub.EW (α,θ)/A.sub.NS (α,θ)≡tanζ                         (3)

where ζ is an "indicated angle" which, for a wavefront of wavelength, λ,incident at azimuth θ and elevation angle α, is given by ##EQU1##As forthe elevation angle, a, we formulate the expression ##EQU2##Thedifferences (ζ-θ) and (γ-α) represent "instrumental" errors in treatingζ as the azimuth angle θ and γ as the elevation angle α. These errorsare called spacing errors, and limiting them, for a given number ofantennas in the cluster (4, in the preceding derivations), requires thatwe limit the value of D/λ, the aperture of the cluster.

It should be noted that spacing errors, because of their systematic,fixed instrumental nature, can be calibrated out, at the cost of astorage requirement, provided they are limited to manageable levels bydesign. It will be shown, however, that the spacing errors can bereduced to negligible levels if the number of antennas in the cluster ismade large enough, even for antenna spacing (cluster diameter) ofseveral wavelengths, except for certain discrete values of antennaspacing at which the maximum magnitude of the spacing error is π/2 rad.

It is clear from the restriction on antenna separation in Eqs. (5) and(7) that the proper polar patterns for the two A-pair combinations in a4-element cluster to ensure that ζ=θ and γ=α, are

In azimuth, a cos θ pattern, for the N-S sensor, and a sin θ pattern forthe E-W sensor;

In elevation angle, a cos² α pattern for both.

The cos θ and sin θ patterns are depicted each by a pair of tangentiallytouching circles forming a "figure-of-eight". Values of D/λ in excess of1/4 cause very noticeable departures from the figure-of-eight shape.These departures cause ζ in Eq.(4) to become significantly differentfrom θ, and γ in Eq.(6) to become significantly different from α; and,hence, the interpretation of ζ as θ in Eqs.(3) and (4), and of γ as α inEqs.(6)and (7), become subject to significant "spacing errors."

We state and demonstrate the following

Theorem: Except for an infinite set of disallowed, discrete values ofD/λ, it is possible to synthesize an A_(NS) (α,θ,n) pattern and anA_(EW) (α,θ,n) pattern from the n/2 A-pair outputs of n antennasarranged with uniform spacing around a circle of radius D/λ, such that##EQU3##

It can be shown (Ref. 1) that if the differenced outputs of a sufficientnumber of diametrically opposite pairs of antennas are combined in aprescribed way, then, except for a sequence of forbidden discrete valuesof D/λ, we can synthesize two resultant signals described by

    e.sub.NS (t)=(n/2)E.sub.s (πD/λ){cos.sup.2α cosθ}sinω.sub.c t,                            (9a)

Corresponding to a North-South diameter and

    e.sub.EW (t)=(n/2)E.sub.s (πD/λ){cos.sup.2α cosθ}sinω.sub.c t,                            (10a)

Corresponding to an East-West diameter where n=(even) number of antennasaround the perimeter of the circle

If, further, an antenna is placed at the center of the circle, then itsoutput will be

    e.sub.o (t)=E.sub.s cosαcosω.sub.c t           (11)

The method of synthesis is as as follows. With reference to FIG. 1a),consider a set of n(=even number) antennas arranged with uniform spacingaround a circle of diameter D/λ. The E, N, W, and S positions are calledthe cardinal positions, and the N-S and E-W lines are called thecardinal axes. The addition of antennas at uniformly spaced off-cardinalpositions on the perimeter enables sampling of the signal phase atmirror-image points about the N-S axis, and about the E-W axis. Thesteps for the synthesis are:

1. Designate the N end of the N-S axis as the reference North, andmeasure azimuth angle clockwise from that diameter;

2. Resolve the DDA patterns of the off-diagonal A-pairs into componentsalong the cardinal N-S and E-W axes by

Adding the differenced outputs of all off-cardinal A-pairs, to obtainthe sum of their N-S components, and

Subtracting the differenced outputs of the 2nd→4th-quadrant pairs fromthe differenced outputs of the 1st→3rd-quadrant pairs, to obtain the sumof their E-W components.

3. Define

    A.sub.NS (α,θ,n)=(all DDA's)                   (9b)

    A.sub.EW (α,θ,n)=Σ(E-W & 1st→3rd-Quadrant pair DDA's)-Σ(2nd→4th-Quadrant pair DDA's)        (10b)

The values of D/λ for which the convergences stated in the theorem willoccur are determined from the expression for the maximum spacing errorin interpreting ζ as θ. Let

    ε.sub.θ,sp,max ≡Maximum Spacing Error in θ=|ζ-θ|.sub.max

Then it can be shown {1} that, for

    0<β<Value for First Peak of J.sub.n-1 (β)        (12)

    tanε.sub.θ,sp,max ≅|J.sub.n-1 (β)/J.sub.1 (β)|                       (13)

where J_(n) (β) is the Bessel function of the first kind, n-th orderandargument β, and

    β≡π(D/λ)cosα=πD/λ, for α=0 (14)

The convergences stated in the Theorem follow from the fact that thelimit of the right-hand side of Eq.(13) as n goes to infinity is zero,except for values of β at which J₁ (β)=0; i.e.;

    tanε.sub.θ,sp,max →0 as n→∞, for J.sub.1 (β)=0

J_(n-1) (β) is nonzero for all β included in (12). (In any case, thezeros of J_(n-1) (β) and J₁ (β) occur at different values of β.) At thezeros of J₁ (β),

    ε.sub.θ,sp,max =π/2, independently of n   (15)

Thus, the convergence of tan ζ to tan θ as n→∞ willnot occur for valuesof D/λ that correspond to the zeros of J₁ (β). For β>0, J₁ (β)=0 atvalues of β corresponding to ##EQU4##These values apply, of course, forα=0, and in view of Eq.(14), will hold very approximately for|α|<0.45≅π/7 rad. Otherwise, the values of D/λ that must be excludedwill shift upward as α→π/2.

The excluded point values of D/λ

a) Divide the range of useable values of D, for a given λ (or itscorresponding frequency), into subranges each of extent equal verynearly to λ; and

b) Divide the frequency range for which acceptable DF performance isrealizable, with a given D, into bands each of width approximately c/DHz,where c is the velocity of propagation. For D=1 m, c/D=300 MHz.

In a practical design, the number of antennas is determined in light ofEq.(13) to satisfy a specified tolerance on ε.sub.θ,sp,max <<1.Specifically,

i) The value of D/λ is chosen to fall within the desired allowedsubrange, as close to a local peak of |J₁ (β)|as possible; and

ii) The value of n is then chosen so that J_(n-1) (β) is sufficientlysmall to satisfy the bound

    |J.sub.n-1 (β)/J.sub.1 (β)|<ε.sub.θ,sp,max <1        (17)

For D/λ<1.22, the first range of allowable A-pairwise antenna spacing(for α<π/7 rad), upper-bounded by the first nonzero zero of J₁ (β), thevariation of the maximum allowable spacing, D_(max), with the number, n,of antennas in the cluster, for the spacingerror in azimuth not toexceed a specified value is monotonically increasing for verticallypolarized wavefronts incident at zero elevation angle. As D approachesan excluded value, the spacing error, with n not sufficiently large,grows rapidly to the absolute maximum of π/2 rad. Upon reaching aforbidden separation the spacing error becomes independentof n, and agoniometer-type of bearing indicator (i.e., one that computes ζ andpresents it as θ) breaks down. The physical reason for this breakdowncan be determined by examining the radial pattern for a single Adcockpair.DDA polar plots show that as D/λ increases (either because D isincreased for the same λ, or λ is decreased for the same D) startingfrom a very small value, the pattern starts as very nearly two circlestouching at the origin, develops dimplesabout θ=0 and π as D/λ becomesgreater than 1/4, the dimples deepening down to nulls at θ=0 and π forD/λ=1, atwhich point each of the originally single lobes splits up intotwo lobes with the same phase. However, as, D/λ becomes greater thanone, theDDA polar pattern plots as a function of θ show that new lobeswith phase opposite to the others emerge about θ=0 and π, which growuntil for D/λ=1.22, these new lobes reach a level comparable with thatof the two lobes resulting from the two nulls at θ=0 and θ=π. Thus, thepattern of each pair acquires deformities that cannot becompensated/repaired in combination with any number of otherintermediate pairs.

For values of β not restricted as in Eq.(12), ##EQU5##Based on thisexpression, values of D/λ can be considered in subranges beyond thosethat fit below the right-side bound in Eq.(12). Thecluster designguidelines for ensuring a wide aperture with a specified tolerance onspacing error become:

i) Choose a value of D/λ in between zeros, and preferably near a peak ofthe magnitude, of

    J.sub.1.sup.2 (β)-4{J.sub.n.sup.1 (β)}.sup.2     (19)

ii) Choose n so that J_(n-1) (β) is very near to, or at, one of itszeros for the chosen value of D/λ.

In Adcock-type differencing of phasor outputs of diametrically separatedpairs of antennas, a D/λ>1 does not cause cyclic-ambiguity because i)A_(NS) (α,θ,n) and A_(EW) (α,θ,n) are detected/measured as cyclicallyunambiguous amplitudes or voltages, unlikecyclically ambiguous phasedifferences; ii) Azimuth θ is a one-cycle angles iii) Elevation angle ais a one-quarter-cycle angle.

A multi-λ separation between antennas whose output phasor differenceistaken will cause only the multilobing effect in the measured DDA's thatwe have sought to compensate for with "gap-filling" additional A-pairs.

However, a quadrantal ambiguity of bearing (azimuth) indication willarise in inverting tan ζ. This ambiguity is resolved by means of a"sense signal" obtainable either a) by adding a centrally mounted "senseantenna"to the circularly arranged cluster; or b) by taking the sum ofsome or all individual antenna outputs as the "sense signal." In eitherway, the sensesignal derived establishes a reference phase thatcorresponds to the physical center of the cluster circle.

The quadrantal ambiguity in tan⁻¹ (. . . ) is resolved in effect byemploying the sense signal as the carrier phase reference for deriving(byproduct demodulation, direct or in an APC demodulator) thedirection-dependent amplitudes(DDA's) of the composite N-S and E-Wsignals. The polarities of the DDA output voltages are determined by thephases of the A-pair output signals relative to the π/2-phase-shiftedsense signal. These polarities, of course, resolve the quadrantalambiguity.

The various outputs of the n/2 A-pairs of an n-antenna cluster may beprocessed separately in an (n/2)-channel receiver; or they may bemultiplexed in some manner so that they may be processed in asingle-channel receiver; or they may be operated on by passive circuitryin the front-end to derive (in Block 5, FIG. 1a))

    A.sub.NS (α,θ,n)sinω.sub.c t, A.sub.EW (α,θ,n)sinω.sub.c t                     (20)

and the sense signal, E_(s) cosαcosω_(c) t which can then be processedeither through a 3-channel receiver, or through a multiplexerfollowed bya single-channel receiver(Blocks 8 and 9, FIG. 1b).

The problems of ensuring identical, separate receiver channels arepractically eliminated by frequency multiplexing the variousDDA-carrying signals in Block 8, FIG. 1b), within a very narrowbandwidth of a single-channel receiver, or by switching the input ofsuch a receiver between the various DDA-carrying signals, in Block 8 ofFIG. 1b).

In the variations, such as exemplified in FIG. 2, on the choice ofrelativepositions of elements that are A-paired around the arrayperimeter 7, as well as of shape 7 of perimeter, the relativeorientation angles ±β₁, ±β₂, . . . , are chosen so that the major lobesof the DDA's within the directional sector of interest centered aboutthe orientation of the axis A-B combine to shore up one another'sfalling skirts. The directional preference can be steered in the exampleof FIG. 2a) by moving the role of the one "focal" antenna, A, that iscommon to all pairs, to other antenna positions around the perimeter.Other embodiments of this invention which illustrate alternative A-pairfocalization arrangements are shown in FIGS. 2c) and d).

The preceding analyses were predicated on the incident signal containinganisolated, filter-separable single-frequency component. The simplestway to extend the results to a modulated signal that does not offer sucha component on arrival is to start by "dismodulating" the signal;i.e.,suppressing the modulation to restore a filter-separable,single-frequency "sinusoidal carrier" component, which may also bedescribed as despreadingthe incident-signal spectrum down to asingle-frequency carrier. It is preferred that this signal dismodulationor spectrum-despreading process be effected at the earliest convenientreception stage. A sense antenna, C, would greatly facilitate thisprocess by providing the dismodulating signal. The output of a senseantenna is applied as is in the manner illustrated in the embodiment ofthis invention shown in FIG. 3a) for constant-envelope signals. Withreference to FIG. 3a), the sense antenna, C, output is firstfrequency-shifted by means of Frequency Shifter 13 by afixed amountf_(if) determined by Oscillator 14, and then applied to Multipliers 15to multiply each of the A-pair phasor-difference outputs 4 ofPhasor-Differencers 3. The frequency-difference-component of each of theresulting products will be stripped of any phase or frequencymodulation, and will appear in the output of the corresponding Ampfilter16 as a single-frequency sinewave with amplitude proportional to the DDAof the phasor-difference signal 4, multiplied by cos α. This phase orfrequency modulation wipeoff process may alternatively be applied to theouput of each of the individual antennas in the array 1, or to eachofthe phasor-difference signals 4 after each has been operated on to becommitted to a sub-channel slot (in frequency, time, code, tone, orother), before or after the sub-channels are combined to yield themultiplexed combination.

As for a single-frequency sense-antenna signal 7 (FIGS. 1 and 3), thesense-antenna output may be operated on separately by a Sense-SignalModulation Suppressor 17, which employs techniques described in U.S.Pat. No. 4,513,249 and/or other coded-spread-spectrum despreadingtechniques. Alternatively, a combination of some or all of thedismodulated DDA-carrying signals may be combined to synthesize asingle-frequency sense signal.

Combined AM and FM signals may be dismodulated by using the techniquesof U.S. Pat. No. 4,513,249. In such a case, the sense-antenna output isfirstconverted into a "modulation wipeoff auxiliary signal," namely onewhose envelope is the reciprocal of the envelope of the incident signal,and whose instantaneous frquency is f_(if) plus the instantaneousfrequency of the incident signal. The modulation wipeoff auxiliarysignal is then applied to Multipliers 15 to multiply each of the A-pairphasor-differenceoutputs 4.

In noncircular arrangements, as for examples 1 in FIGS. 1b), c), d) ande),and FIG. 3b),each A-pair may be provided with a separate senseantenna placed at mid-point (C₁, C₂, . . . in FIG. 3b), loci 9 in FIGS.2a) and b)) between their positions.

REFERENCE

1. Redgment, P. G., Struszynski, W., and Phillips, G. J., "An Analysisof the Perfromance of Multi-Aerial Adcock Direction-Finding Systems,"Journalof IEE, vol. 94, Part III A, pp. 751-761; 1947.

While there has been described what is at present considered to berepresentative embodiments of the invention, it will be obvious to thoseskilled in the art that various changes and modifications may be madetherein without departing from the invention, and it is aimed in theappended claims to cover all such changes and modifications as fallwithinthe true spirit and scope of the invention.

For clarity in the statements of the appended claims, the followingdefinitions of terms are provided:

Adcock array is characterized by four features: a) Circular, with orwithout a center element usually called a sense element; b)Uniformlyspaced elements along perimeter of circle; c)Total, or phasor, ofoutputs of diametrically separated elements are subtracted one from theother, resulting in phasor-difference outputs; d)Diameter of circle isless than 1.22 times the shortest wavelength for which the array isdesigned.

Adcock-array way, is one characterized by a), b) and c) only.

Inverting envelope waveform means transforming a combined envelope andexponent (phase or frequency) modulated signal represented byV(t)cos{ω_(c) t+ψ(t)} to {1/V(t)}·cos{ω_(c) t+ψ(t)}. The latter,shiftedf_(if) Hz, is called "auxiliary modulation-wipeoff signal".

Diametrically separated means positioned at the ends of the samediameter of a circle.

Focal element is an element whose output is subtracted from the outputsof more than one element of an array.

Conic section means circle, or ellipse, or or parabola, or hyperbola.

Matricial means arranged in the form of a matrix, including a straightline(a row or column matrix) and more generally an mxn array(rectangular, triangular, square, etc.).

What is claimed is:
 1. A method for determining the azimuth andelevation angles of the direction of arrival of a travelling signalwavefront of measurable wavelength, λ, comprising the steps of:employinga noncircular array of discrete sensor elements; taking aphasor-difference between the outputs of pairs of spaced elements, saidphasor-difference being a function of the azimuth and elevation anglesof arrival of said travelling signal wavefront; and deriving from saidphasor-difference the azimuth and elevation angles of the direction ofpropagation of said signal wavefront relative to angle referencesassociated with said array.
 2. The method of claim 1, wherein said arraycomprises one group of elements spaced along a noncircular conicsection, and one or more other separate elements.
 3. The method of claim2, wherein said array comprises one group of elements spaced along aconic section, and one or more other separate elements at least one ofwhich is focal.
 4. A method for determining the azimuth and elevationangles of the direction of arrival of a travelling signal wavefront ofmeasurable wavelength, λ, comprising the steps of:utilizing an array ofdiscrete sensor elements arranged with nonuniform spacing around acircle; taking a phasor-difference between the outputs of pairs ofspaced elements, said phasor-difference being a function of the azimuthand elevation angles of arrival of said travelling signal wavefront; andderiving from said phasor-difference the azimuth and elevation angles ofthe direction of propagation of said signal wavefront relative to anglereferences associated with said array.
 5. The method of claim 4, whereinphasor-differences are taken between diametrically separated elements.6. The method of claim 4, wherein, phasor-differences are taken betweenat least one focal element and a plurality of additional elements insaid array.
 7. A method for determining the azimuth and elevation anglesof the direction of arrival of a travelling signal wavefront ofmeasurable wavelength, λ, comprising the steps of:utilizing an array ofdiscrete sensor elements, some of which arranged along an arc of a conicsection, others of which are arranged off of the conic section; taking aphasor-difference between the outputs of pairs of spaced elements; andderiving from said phasor-difference the azimuth and elevation angles ofthe direction of propagation of said signal wavefront relative to anglereferences associated with said array.
 8. The method of claim 7, whereinphasor-differences are taken between at least one focal element and aplurality of additional elements in said array.
 9. An apparatus fordetermining the azimuth and elevation angles of the direction of arrivalof a travelling signal wavefront of measurable wavelength, λ,comprising:an array of discrete sensor elements, some of which arrangedalong an arc of a conic section, others of which are arranged off theconic section; means for taking a phasor-difference between the outputsof pairs of spaced elements; and means for deriving from saidphasor-difference the azimuth and elevation angles of the direction ofpropagation of said signal wavefront relative to angle referencesassociated with said array.
 10. The apparatus of claim 9, whereinphasor-differences are taken between at least one focal element and aplurality of additional elements in said array.
 11. A method fordetermining the azimuth and/or elevation angle(s) of the direction ofarrival of a travelling signal wavefront of measurable wavelength, λ,comprising the steps of:utilizing any of a multiplicity of planar arraysof discrete sensor elements with a linear dimension, or separation,between at least two elements, that exceeds 1.22λ; taking aphasor-difference between the outputs of pairs of spaced elements toproduce a set of phasor differences; transforming said set of phasordifferences into a resultant three-dimensional vector pointing in adirection of propagation of said signal wavefront; identifying theazimuth and elevation angles of arrival of the signal wavefront relativeto an angle reference system associated with any of said multiplicity ofplanar arrays.
 12. A method for determining the azimuth and/or elevationangle(s) of the direction of arrival of a travelling signal wavefront ofmeasurable wavelength, λ, comprising the steps of:utilizing atwo-dimensional, circular array of discrete sensor elements with alinear dimension, or separation, between at least two elements, thatexceeds 1.22λ; taking a phasor-difference between the outputs of pairsof spaced elements to produce a set of phasor differences; transformingsaid set of phasor differences into a resultant three-dimensional vectorpointing in a direction of propagation of said signal wavefront:identifying the azimuth and elevation angles of arrival of the signalwavefront relative to an angle reference system associated with saidarray, said step of transforming further including the steps of:derivingfrom said set of phasor differences a resultant East-West and aresultant North-South phasor; and combining said resultant East-West andNorth-South phasors to derive an azimuth of the direction of propagationof said signal wavefront relative to a reference North-South direction,and/or an elevation of angle of the direction of propagation relative toa reference plane associated with said array.
 13. The method claim 11,wherein said array is two-dimensional, and said step of transformingcomprises using an array- or a matrix-processing algorithm.
 14. Themethod of claim 11, wherein said array includes at least a planar arrayhaving a first orientation and another linear or planar array having asecond orientation different from the first orientation, and said stepof transforming comprises:deriving from said set of phasor-differences aresultant East-West phasor, a resultant North-South phasor and aresultant Zenith-Nadir phasor; and combining said East-West, North-Southand Zenith-Nadir resultant phasors to derive an azimuth of the directionof propagation of said signal wavefront relative to the referenceNorth-South direction, and an elevation angle of the direction ofpropagation relative to a reference plane associated with said array.15. The method of claim 11, wherein said array includes at least aplanar array having a first orientation and another linear or planararray having a second orientation different from the first orientation,and said step of transforming comprises a multi-dimensionalarray-processing algorithm.